Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary.
cos θ = 0.8192 A = 45 H = ?
The given values in the problem are cos θ = 0.8192, A = 45 degrees, and we need to find H.
Since we have cos θ, we can use the definition of cosine to find the adjacent side (A) and the hypotenuse (H):
cos θ = A/H
0.8192 = 45/H
To solve for H, we can multiply both sides of the equation by H:
0.8192H = 45
Divide both sides of the equation by 0.8192:
H = 45/0.8192
Using a calculator, we find that H ≈ 54.93.
Rounding to the nearest degree, H ≈ 55 degrees.
To find the angle θ, we can use the inverse cosine function (arccosine) since we know the value of cos θ.
Using a table of trigonometric values or a calculator, we can find the angle whose cosine is approximately 0.8192.
arccos(0.8192) ≈ 35.505 degrees (rounded to the nearest degree)
Therefore, the angle θ is approximately 35 degrees.